IMO Shortlist 1999 problem N3
Dodao/la:
arhiva2. travnja 2012. Prove that there exists two strictly increasing sequences
![(a_{n})](/media/m/2/e/8/2e8c10df3c543ec89c52ae33974809f3.png)
and
![(b_{n})](/media/m/5/f/7/5f72594f4283cc3bf5320d92eea618cd.png)
such that
![a_{n}(a_{n}+1)](/media/m/4/1/0/41014892d29914ab5596694a4d9b2168.png)
divides
![b^{2}_{n}+1](/media/m/c/b/3/cb34fb1d5a37ca39ced52ca8329b1a0a.png)
for every natural n.
%V0
Prove that there exists two strictly increasing sequences $(a_{n})$ and $(b_{n})$ such that $a_{n}(a_{n}+1)$ divides $b^{2}_{n}+1$ for every natural n.
Izvor: Međunarodna matematička olimpijada, shortlist 1999